Nearly everyone has a video camera on their cell phone, ready to record at a moment’s notice. The police encounters that caused the deaths of Walter Scott, Tamir Rice, Eric Garner and others have been captured on such cameras. Human recall and memory is fallible, and because of that, video is often the best documentation of what actually occurred between police and the person they are interacting with.
Video footage protects citizens and officers alike, and many police departments are taking steps to have officers wear body cameras or use in-car video systems for this very reason.
If an officer is interacting with someone in a public space, you have an absolute right to record the encounter, provided that you do not interfere with the officer in the performance of their duty. What constitutes “interference” is not clearly defined, but as a general rule, anyone recording a police encounter should not do anything that would require the officer to divert their attention to the person with the camera. Recording should be done from a safe distance, and the person recording should be aware that their actions may not be welcome by the officer or the person they are interacting with.
Here are a few articles that discuss the issue:
http://www.npr.org/2011/05/13/136171366/this-is-the-police-put-down-your-camera